Studies on the mathematical simulation of mass transfer in the microcirculation have been carried out for a number of years starting with Krogh's early work. In almost every case the continuum approach has been used. This is to say that blood has been treated as a single homogeneous fluid despite the fact that the undeformed erythrocytes are of maximum diameter greater than the capillaries. Results of recent theoretical investigators under the direction of the present writer show that it is possible to predict the dimensions and velocities of the deformed erythrocytes in the flow in capillaries. It is now proposed to solve the diffusion and convection problem taking the presence of the erythrocytes into account. It is shown that the results will differ significantly from those from the continuum approach over certain ranges of the parameters--especially in the case of oxygen transport. The results will help place the important field of research on simulation of the microcirculation on a stronger base.